"Heat Equation Derivative Formulas for Vector Bundles," by B. Driver
and Anton Thalmaier.
(UCSD and Univ. of Bonn Preprint, March 2000, and 1998 )
Available as a DVI
file (284K) or a PDF file (769K).
Abstract
We use martingale methods to give Bismut type derivative formulas
for differentials and co-differentials of heat semigroups on forms, and more
generally for sections of vector bundles. The formulas are mainly in terms
of Weitzenb\"{o}ck curvature terms, in most cases derivatives of the
curvature are not involved. In particular, our results improve the formula
in Driver \cite{Driver:97b} for logarithmic derivatives of the heat kernel
measure on a Riemannian manifold. Our formulas also include the formulas in
Elworthy and Li \cite{Elworthy-Li:98}.
March 2000
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